You don't get it? I guess not.
When I say a standardized battery pack, I'm obviously not talking about what's currently in an electric car, for the reasons you point out. Let's leave the notion of a standard combustion engine car's battery out of it, it's not relevant to the discussion. The battery pack is not going to be embedded in the body of the car, or underneath it, like current EVs.
The battery pack is not going to have simple terminals. These theoretical batteries are modular, they snap in, think batteries like on a digital camera, or a phone with replaceable batteries, but larger. Maybe by the time we get around to this, battery technology will have provided us with a much lighter battery. And if batteries are still heavy, perhaps you have a robotic system that can remove the discharged battery, and place a fresh battery into the battery receptacle. Or maybe you have the modern version of a gas station attendant who operates a lift-assist device for the swap.
As for your notion of 'buy-in to the idea of "community use" of a shared asset that degrades over time', there are ways to deal with these issues, such as monitoring battery health and pulling failing batteries out of the stream. Or maybe the battery pack isn't part of the car at sale, much like the first tank of gas you get from the dealership when you buy a car, you get a battery pack with whatever charge is in it, and replace as necessary. Maybe the charge station company charges an annual fee for battery pack maintenance and replacement. Maybe that cost is part of the cost for the swap at the "pump".
You're looking at things as they are currently, and the way things are currently is not going to work. Nobody is going to want to wait half an hour while their car charges during their commute. (What if your commute starts from the person you picked up at the bar after work's apartment, where you parked on the street, having not charged to full capacity previously.)
Live within your income, even if you have to borrow to do so. -- Josh Billings